Quantum circuit compilation and hybrid computation using Pauli-based computation

Abstract

Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. Any quantum circuit written in terms of the Clifford+$T$ gate set and having $t$ $T$ gates can be compiled into a PBC on $t$ qubits. Here we propose practical ways of implementing PBC as adaptive quantum circuits and provide code to do the required classical side-processing. Our schemes reduce the number of quantum gates to $O(t^2)$ (from a previous $O(t^3/\log t)$ scaling) and space/time trade-offs are discussed which lead to a reduction of the depth from $O(t\log t)$ to $O(t)$ within our schemes, at the cost of $t$ additional auxiliary qubits. We compile examples of random and hidden-shift quantum circuits into adaptive PBC circuits. We also simulate hybrid quantum computation, where a classical computer effectively extends the working memory of a small quantum computer by $k$ virtual qubits, at a cost exponential in $k$. Our results demonstrate the practical advantage of PBC techniques for circuit compilation and hybrid computation.

28 pages, 14 figures, includes links to a GitHub repository for Python software implementing all tasks discussed in the paper

References in corpus (12)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum algorithm for solving linear systems of equations
• Surface codes: Towards practical large-scale quantum computation
• Quantum computational advantage using photons
• Strong quantum computational advantage using a superconducting quantum processor
• Resource-efficient linear optical quantum computation
• Application of a resource theory for magic states to fault-tolerant quantum computing
• High-speed linear optics quantum computing using active feed-forward
• CutQC: Using Small Quantum Computers for Large Quantum Circuit Evaluations
• Circuit knitting with classical communication
• Fast quantum circuit cutting with randomized measurements
• Pauli-based model of quantum computation with higher-dimensional systems

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• Simulating quantum computation: how many "bits" for "it"?
• Simulation of quantum computation with magic states via Jordan-Wigner transformations
• Reducing depth and measurement weights in Pauli-based computation
• Polynomial-Time Classical Simulation of Hidden Shift Circuits via Confluent Rewriting of Symbolic Sums
• Symmetry-Accelerated Classical Simulation of Clifford-Dominated Circuits